We solve the problem of choosing the minimum number of measurement points t1,...,tn in an interval [a, b] which are required for constructing polynomial Pn(t) with minimum deviation from a given trajectory f (t). We also consider the problem of optimal sensor placement. The solutions of these problems for the two- and three-dimensional cases are optimal in the sense of uniform approximation of functions and have the advantages of the least squares method.
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 90–98, 1987.
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Tsitritskaya, L.N. Choosing trajectory sections with highest information content for a dynamic system. J Math Sci 63, 579–585 (1993). https://doi.org/10.1007/BF01142534
- Dynamic System
- Measurement Point
- Information Content
- Minimum Deviation
- Uniform Approximation